Mathematical Operations problems
- 1. Statements:
A > B, B ? C = D < E
Conclusions:
I. C < A II. D ? B
Options- A. If only conclusion I follows
- B. If only conclusion II follows
- C. If either conclusion I or II follows
- D. If neither conclusion I nor II follows Discuss
Correct Answer:
Explanation:
If both conclusion I and II follow.
- 2. Statements:
H > J = K, K ? L, L > T, T < V
Conclusions:
I. K > T II. L ? H
Options- A. If only conclusion I follows
- B. If only conclusion II follows
- C. If either conclusion I or II follows
- D. If neither conclusion I nor II follows Discuss
Correct Answer: If only conclusion I follows
Explanation:
If only conclusion I follows
- 3. Statements:
A ? B = C, D > C = E
Conclusions:
I. E > A II. A < D
Options- A. If only conclusion I follows
- B. If only conclusion II follows
- C. If either conclusion I or II follows
- D. If neither conclusion I nor II follows Discuss
Correct Answer: If either conclusion I or II follows
Explanation:
If either conclusion I or II follows
- 4. Statements:
A ? B = C, B < D ? E
Conclusions:
I. D > A II. E > C
Options- A. If only conclusion I follows
- B. If only conclusion II follows
- C. If either conclusion I or II follows
- D. If neither conclusion I nor II follows Discuss
Correct Answer: If only conclusion II follows
Explanation:
A ? B = C < D ? E
I. D > A is not true, II. E > C is true.
- 5. Statements:
L > U ? K, Z < U < R
Conclusions:
I. L > Z II. K < R
Options- A. If only conclusion I follows
- B. If only conclusion II follows
- C. If either conclusion I or II follows
- D. If neither conclusion I nor II follows Discuss
Correct Answer:
Explanation:
Split them as L > U ...(i)
Combining (i) and (ii),
We get L > U > Z or L > Z
Hence I follows.
Combining (ii) and (iv) we get K ? U < R or K < R Hence II follows.
- 6. Statements:
Y < J = P ? R > I
Conclusions:
I. J > I II. Y < R
Options- A. If only conclusion I follows
- B. If only conclusion II follows
- C. If either conclusion I or II follows
- D. If neither conclusion I nor II follows Discuss
Correct Answer: If only conclusion I follows
Explanation:
Y < J = P ? R > I
I. J > I is true, II. Y < R is not true.
- 7. Statements:
V ? K > M = N, M > S, T< K
Conclusions:
I. T < N II. V = S
Options- A. If only conclusion I follows
- B. If only conclusion II follows
- C. If either conclusion I or II follows
- D. If neither conclusion I nor II follows Discuss
Correct Answer: If neither conclusion I nor II follows
Explanation:
V ? K > M = N > S
K > T
I. T < N is not true, II. V = S is true.
- 8. Statements:
F ? X < A, R < X ? F
Conclusions:
I. F ? E II. R < F
Options- A. If only conclusion I follows
- B. If only conclusion I follows
- C. If either conclusion I or II follows
- D. If neither conclusion I nor II follows Discuss
Correct Answer: If only conclusion I follows
Explanation:
Split them as F ? X ...(i) X < A ...(ii)
R < X ...(ii) and X ? E ...(iv)
Combining (i) and (iv) we get
F ? X ? F or F ? E.
Hence I follow.
From (i) and (iii) R and F can't be compared. Hence II does not follow.
- 9. Which of the following sets of operation with the usual notations replacing the starts in the order given makes the statements valid?
? 100 * ? 16 * ? 225 * ? 1
Options- A. x, =, +
- B. +, =, -
- C. +, =, x
- D. -, x, = Discuss
Correct Answer: +, =, -
Explanation:
?100 + ?16
= ?225 -?1
10 + 4 = 15 - 1
? 14 = 14
- 10. Select the correct combination of mathematical signs to replace '*' signs and to balance the given equation.
24 * 34 * 2 * 5 * 12
Options- A. + ÷ x =
- B. = ÷ + -
- C. = ÷ - +
- D. + ÷ = x Discuss
Correct Answer: = ÷ - +
Explanation:
From option (c),
24 = 34 ÷ 2 - 5 + 12
? 24 = 17 - 5 + 12
? 24 = 29 - 5
? 24 = 24
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